Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

Table of figures

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              Cap. 12. dę
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              vacui neceſ­
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              ſitate.</s>
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              <s id="s.002848">HInc deducitur, quòd ſi concurrant apices angu­
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              lorum plurium figurarum planarum ad vnum
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              punctum plani ſubiecti, illę ſpatium omninò com­
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              plebunt, quotieſcumque æquales quatuor angulis
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              rectis fuerint, ſin minùs aut penetratio in exceſſu, aut
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              interſtitia inania in defectu relinquere debent. </s>
              <s id="s.002849">Quia
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              verò figurarum planarum aliæ regulares ſunt, ſcilicèt
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              æquiangulæ, & æquilaterę, aliæ irregulares,
                <expan abbr="cõſtat">conſtat</expan>
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              ex Theone, Pappo, Maurolico, & alijs, ſex angulos
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              regularium triangulorum ad vnum punctum plani
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              ſubiecti concurrentes ſpatium implere, eò quòd
                <expan abbr="sũ-mam">sum­
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                mam</expan>
              quatuor rectorum adæquant, ſic etiam apices
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              quatuor angulorum quadratarum figurarum ad
                <expan abbr="vnũ">vnum</expan>
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              punctum eiuſdem plani concurrentes ſpatium com­
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              plent, non ſecùs apices trium angulorum hexagona­
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              lium figurarum, paritèr ſpatium adimplent, & nullæ
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              aliæ; figurarum verò irregularium anguli ad vnum̨
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              punctum ſpatij plani concurrentes, qui ſpatium
                <expan abbr="cõ-plere">con­
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                plere</expan>
              poſſunt propemodum infinitę ſunt, ſcilicèt om­
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              nes illæ, quorum anguli conuenientes ſummam qua­
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              tuor rectorum æquant. </s>
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              <s id="s.002850">Eaſdem proprietates habent anguli ſolidi, qui in
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              vno plano ſuis faciebus adaptari poſſunt, vt ſunt priſ­
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              mata rectangula, & nonnulla alia, quorum baſes, aut
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              ſunt poligona regularia, aut non, & quando anguli
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              baſium ad vnum punctum plani ſubiecti concurren­
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              tes ſpatium prædictum planum complent, etiam ſu­
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              perficies planæ laterales in communi latere erecto
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              conueniunt, & tunc componunt, veluti
                <expan abbr="pauimentũ">pauimentum</expan>
              , </s>
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